• 제목/요약/키워드: Galois group for subfactors

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ON GALOIS GROUPS FOR NON-IRREDUCIBLE INCLUSIONS OF SUBFACTORS

  • Lee, Jung-Rye
    • 대한수학회논문집
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    • 제14권1호
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    • pp.99-110
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    • 1999
  • We apply sector theory to obtain some characterization on Gaois groups for subfactors. As an example of a non-irreducible inclusion of small index, a locally trivial inclusion arising from an automorphism is considered and its Galois group is completely determined by using sector theory.

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GALOIS CORRESPONDENCES FOR SUBFACTORS RELATED TO NORMAL SUBGROUPS

  • Lee, Jung-Rye
    • 대한수학회논문집
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    • 제17권2호
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    • pp.253-260
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    • 2002
  • For an outer action $\alpha$ of a finite group G on a factor M, it was proved that H is a, normal subgroup of G if and only if there exists a finite group F and an outer action $\beta$ of F on the crossed product algebra M $\times$$_{\alpha}$ G = (M $\times$$_{\alpha}$ F. We generalize this to infinite group actions. For an outer action $\alpha$ of a discrete group, we obtain a Galois correspondence for crossed product algebras related to normal subgroups. When $\alpha$ satisfies a certain condition, we also obtain a Galois correspondence for fixed point algebras. Furthermore, for a minimal action $\alpha$ of a compact group G and a closed normal subgroup H, we prove $M^{G}$ = ( $M^{H}$)$^{{beta}(G/H)}$for a minimal action $\beta$ of G/H on $M^{H}$.f G/H on $M^{H}$.TEX> H/.